Distribution of chains in polymer brushes produced by a grafting from mechanism

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1 SUPPLEMENTARY INFORMATION Distribution of chains in polymer brushes produced by a grafting from mechanism Andre Martinez, Jan-Michael Y. Carrillo, Andrey V. Dobrynin,, * and Douglas H. Adamson, * Department of Chemistry and Polymer Program, Institute of Materials Science, University of Connecticut, Storrs, CT National Center for Computational Science, Oak Ridge National laboratory, Oak Ridge, TN Department of Polymer Science, University of Akron, Akron, OH SI1. Experimental Procedures Calculation of membrane curvature: ImageJ was used to take measurements from an SEM image of an unfunctionalized nylon membrane. Average fiber thickness was 411±132nm. Treating fibers as smooth cylinders, curvature (K) perpendicular to the length of the fiber is the reciprocal of the radius. K = 4.87x10-3 nm -1 Circumference measured as 2π(radius) is 1290±414nm therefore a change of 0.279degrees/nm is experienced in the direction perpendicular to length of the fiber. 1

2 Br 3d C 1s O 1s N 1s Binding Energy (ev) Figure SI1: XPS spectrum of unfunctionalized (red) and initiator functionalized (blue) membranes. Inset, the region from 150eV to 0eV has been expanded. Electrons from the oxygen, nitrogen and carbon 1s shell were detected in both samples. Electrons from the bromine 3d shell were detected only in the initiator functionalized sample. 2

3 1.2 : : 1 Figure SI2: H 1 -NMR of solutions of BrIbB, IbB, and triethylamine in deuterated chloroform. The reacted (red) sample contained cryogenically ground nylon that was not dissolved but reacted with the acid bromides. Changes in the BrIbB/IbB methyl peak area ratios indicate BrIbB is more reactive. Table S1: Calculation of PMMA grafting density of sample C4 based upon average fiber diameter before and after polymerization. Sample Average fiber diameter (nm) Average brush height (nm) Grafting density (chains/nm 2 ) Unmodified 411±132 N/A N/A Membrane C4 978±

4 Figure SI3: Samples C1-C4 from Table 2 after PMMA grafting. From left to right 30%initiator, 50%initiator, 75%initiator, 100%initiator. 35k PMMA Normalized Intensity 35k PMMA base treatment Retention Time (min) Figure SI4: GPC of commercially available 35kg/mol PMMA before and after treatment with basic conditions used to cleave brushes. Intensiy offset for ease of viewing. 4

$Reaction time (hours) MW of high MW cleaved polymer (Kg/mole) Mass fraction of low MW polymer Number fraction of low MW polymer 2 17.6 0.752 0.964 4 27.$ 5 0.559 0.946 8 20.3 0.273 0.792 The same assumptions and cautions mentioned for table 2 apply to this table as well.

5 0.559 0.946 8 20.3 0.273 0.792 The same assumptions and cautions mentioned for table 2 apply to this table as well.

1: Simulation Details We performed molecular dynamics Figure SI5: Snapshot of the simulation box with growing polymer chains.

simulations of the process of growing polymeric brushes from a substrate.

5 Table S2: Calculation of PMMA grafting density of samples from Figure 6. Reaction time (hours) MW of high MW cleaved polymer (Kg/mole) Mass fraction of low MW polymer Number fraction of low MW polymer The same assumptions and cautions mentioned for table 2 apply to this table as well. SI2: Molecular Dynamics Simulations of Brush Polymerization SI2.1: Simulation Details We performed molecular dynamics Figure SI5: Snapshot of the simulation box with growing polymer chains. Substrate beads are colored in green, catalytic sites are shown in red, and monomers are shown as blue dots. simulations of the process of growing polymeric brushes from a substrate. In our simulations, beadspring chains consisting of Lennard- Jones beads with diameter of modeled the growing brush chains, catalytic sites and monomers. The growing chains were grafted to a substrate located at =0 (see Figure SI5). The substrate consisted of a four-layer lattice of beads with each layer being composed of beads of diameter σ. The substrate had symmetry of the hexagonal closed-packed (HCP) lattice with lattice constant equal to σ. All beads in the system interacted through the WCA potential: 5

4 2 0 2 (S2.1) Figure SI6: Snapshot of the simulation box at the beginning of the simulation run.

Inserts show the location of the grafting points (red) with respect to the substrate beads for three different grafting densities,.

The cutoff distance of rcut = 2 1/6 σ was set for all pair-wise interactions. This corresponds to pure repulsive potential.

6 (S2.1) Figure SI6: Snapshot of the simulation box at the beginning of the simulation run. Substrate beads are colored in green, catalytic sites are shown in red, and monomers are shown as blue dots. Inserts show the location of the grafting points (red) with respect to the substrate beads for three different grafting densities,. (FENE) potential where is the distance between beads, and is the bead diameter chosen to be the same regardless of the bead type. The cutoff distance of rcut = 2 1/6 σ was set for all pair-wise interactions. This corresponds to pure repulsive potential. The interaction parameter was set to for all interactions, where is the Boltzmann constant, and is the absolute temperature. The connectivity of monomers into polymer chains was maintained by the finite extension nonlinear elastic 2 1 = 2 r U FENE( r) ksrm ln S2.2 Rm with the spring constant = 30.0 k B T/σ 2, and maximum bond length 1.5. The repulsive part of the bond potential was modeled by the truncated-shifted WCA potential with the value of LJ-interaction parameter εlj = 1.0 kbt and rcut = 2 1/6 σ. Simulations were carried out in a constant number of particles and temperature ensemble (NVT). The constant temperature was maintained by 6

7 coupling the system to a Langevin thermostat implemented in LAMMPS 1 with GPU acceleration. 2 In this case, the equation of motion of the ith bead is where is the i th bead velocity and is the net deterministic force acting on the bead with mass, which is set as unity for all particles. is the stochastic force S2.3 with zero average value 0 and functional correlations 6. The velocity-verlet algorithm with a time step of was used for integration of equations of motion, where τ = σ(m/εlj) 1/2. We have performed simulations at three different grafting densities = , Figure SI7: Evolution of the monomer conversion during the simulation runs for three different grafting densities, and (see Figure SI6). The catalytic sites from which the brush Figure SI8: Evolution of the logarithm of the ratio of monomer concentrations during simulation runs for different brush grafting densities,. chains were grown were randomly grafted to the substrate by the FENE bonds. Simulations were performed using the following procedure: At the beginning of each simulation run monomers with number density = were uniformly distributed over the volume of the simulation box with dimensions L x =40.00 σ, L y =39.84 σ and L z =83.89 σ. We used periodic boundary conditions in and directions. During the simulation run the substrate beads were excluded 7

8 from the integration of the equation of motion calculation. This kept substrate s beads from moving. We have also added a repulsive Lennard-Jones wall at the top of the simulation box to prevent monomers from escaping. To model the polymerization reaction we have checked the proximity of a monomer to a catalytic site every 2.5. If a monomer was within a cutoff radius 2 / σ from a catalytic site we added a new monomer to a chain by creating a bond. These new added monomers have become a new catalytic site (active monomer) (see Figure SI6). The simulations were continued until all monomers were consumed. The polymerization process was monitored by calculating the monomer conversion during simulation run is shown in Figure SI7. The polymerization scheme is similar to the one employed by Ahn et al. to describe the controlled and living polymerization of poly- Lactide-g-poly-Norbornene bottle-brush macromolecules. 3 We have also performed simulations with chains recombination. In these simulations two chain ends that were within a cutoff radius from each other have been connected by a bond and become a part of the same chain forming a loop attached to the substrate by two ends. We have checked proximity of chain ends every 2.5 τ and 25 τ. This allowed us to perform simulations with fast and slow recombination rates. SI2.2: Simulation Results We will first discuss brush growth kinetics and chain distribution in simulations without ends recombination. One of the main features of addition polymerization or controlled living polymerization, such as ATRP, is that it follows the first-order kinetics 4 [ ] (S2.4) where is the propagation rate, is the instantaneous number density of monomers, is the rate constant and [ ] is the number density of the active propagating species. In the absence of termination events, the solution to eq. S2.4 yields ln 0 [ ] (S2.5) 8

9 The linear dependence of ln with respect to time for the lowest grafting density shown in Figure SI8 indicates that the polymerization behavior is similar to chain growth in solution. Note that at the later stages of polymerization process the curve start slightly deviating from the linear scaling dependence. This could be explained by the finite box size effect beginning to dominate a chain growth at the later stages. Figure SI9: Evolution of the weight fraction distribution of the degree of polymerization, N, during simulation runs. For intermediate and large grafting densities there are three different brush polymerization regimes. At the initial stages we observe an expected linear dependence. At times t>10 2 τ we start to see a slower consumption of monomers which could indicate the decrease in the number of actively propagating species, P*. This could be due to screening of the shorter brush chains by the longer ones. At the later stages of polymerization we again observe a linear dependence but with a different effective constant. In Figure SI9, we plot evolution of the weight fraction distribution S2.6 of the degree of polymerization, N. In eq (S2.6) is a normalized probability distribution to find a chain with degree of polymerization N. For the lowest brush grafting density there are no chains with 1000 at the latest stages of the brush polymerization. This indicates that all chains continue to grow even though the distribution of chains broadens resulting in increase in brush polydispesity. This is not the case for the system with the highest brush grafting density. For such brush we see a very broad chain distribution at the later stages of the brush polymerization. The different mechanisms in the brush polymerization at different 9

10 brush grafting densities are better seen in Figure SI10. This figure clearly indicates the dominance of the shorter chains in the case of the polymerization of the brush with the highest brush grafting density. Also these simulations show that it is impossible to obtain bimodal distribution in P w (N) without chains recombination. Our results for simulations with chains recombination are discussed in the main text. Figure SI10: Time dependence of the probability distribution,, of the degree of polymerization, N. References 1. Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of Computational Physics 1995, 117 (1), Brown, W. M.; Wang, P.; Plimpton, S. J.; Tharrington, A. N., Implementing molecular dynamics on hybrid high performance computers short range forces. Computer Physics Communications 2011, 182 (4), Ahn, S.-k.; Carrillo, J.-M. Y.; Han, Y.; Kim, T.-H.; Uhrig, D.; Pickel, D. L.; Hong, K.; Kilbey, S. M.; Sumpter, B. G.; Smith, G. S.; Do, C., Structural Evolution of Polylactide Molecular Bottlebrushes: Kinetics Study by Size Exclusion Chromatography, Small Angle Neutron Scattering, and Simulations. ACS Macro Letters 2014, Matyjaszewski, K.; Xia, J., Atom Transfer Radical Polymerization. Chemical Reviews 2001, 101 (9),

Radical Polymerization and Click Chemistry. Surfaces using Gamma Irradiation. Supporting Information*

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